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The method of fundamental solutions for a time-dependent two-dimensional Cauchy heat conduction problem
University of Birmingham, England .
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9066-7922
2013 (English)In: Engineering analysis with boundary elements, ISSN 0955-7997, E-ISSN 1873-197X, Vol. 37, no 3, 569-578 p.Article in journal (Refereed) Published
Abstract [en]

We investigate an application of the method of fundamental solutions (MFS) to the time-dependent two-dimensional Cauchy heat conduction problem, which is an inverse ill-posed problem. Data in the form of the solution and its normal derivative is given on a part of the boundary and no data is prescribed on the remaining part of the boundary of the solution domain. To generate a numerical approximation we generalize the work for the stationary case in Mann (2011) [23] to the time-dependent setting building on the MFS proposed in Johansson and Lesnic (2008) [15], for the one-dimensional heat conduction problem. We incorporate Tikhonov regularization to obtain stable results. The proposed approach is flexible and can be adjusted rather easily to various solution domains and data. An additional advantage is that the initial data does not need to be known a priori, but can be reconstructed as well.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 37, no 3, 569-578 p.
Keyword [en]
Heat conduction, Cauchy problem, Inverse problem, Method of fundamental solutions, Regularization
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-92617DOI: 10.1016/j.enganabound.2012.12.008ISI: 000317314400008OAI: oai:DiVA.org:liu-92617DiVA: diva2:621689
Note

Funding Agencies|EPSRC||

Available from: 2013-05-16 Created: 2013-05-14 Last updated: 2017-12-06

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Johansson, Tomas

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